The UK Conservative leader David Cameron says that any Prime Minister not 'directly elected' by the public should be forced to hold a general election within six months. He has in mind his Labour opponent Gordon Brown, who in June 2007 was catapulted into the position by a secret ballot in his own party, rather than by an open election of the people. And if, after the forthcoming general election on May 6, Labour chose to ditch Brown and catapult that gap-year kid...ah, yes, David Miliband...into the top job in order to stitch up a coalition deal with Nick Clegg's Liberal Democrats, well, Cameron would give him only six months to get a public mandate too.

On the surface, this looks like a good idea. Gordon Brown is Prime Minister only because the Labour Party's constitution makes it almost impossible to unseat a leader who doesn't want to go, and since Brown was the real éminance grise behind Blair, no ministerial colleagues wanted to cross him. Those chauffer-driven limos exert a powerful discipline on ministers and would-be ministers.

Look deeper, though, and Cameron's remark reveals how unfit for purpose our constitution has become. Whom Brits elect at a general election is their local MP, not a Prime Minister. The Prime Minister is simply the leader who can then command a majority in the House of Commons. It may not even be the leader of the largest party: if there were a hung parliament, it might be whoever who can mollify different factions and stitch together a workable agreement between them.

But, as with the debates, Britain's political system has now become presidential. Millions of people honestly report that they will be voting for David Cameron, or Nick Clegg, or Gordon Brown – even though only the electors in their own particular constituencies will actually get the chance. The rest of us vote for them by proxy, by choosing one of their party colleagues as our MP. None of our Prime Ministers is 'elected' by the general public.

In the US, the public explicitly choose a President – along with Representatives and Senators. Sure, after deaths and resignations, a Vice President can step into the office, but at least the public knows who to expect. When a UK party leader resigns (or indeed dies), consulting the public is the last thing on the deal-makers' minds. The UK has become a Presidential system with a Parliamentary constitution, and it doesn't work. There is simply nothing to restrain those who take office in Downing Street – who have powers pretty much as wide as George III had.

Making a step-into-the-dead-person's-shoes Prime Minister face an election after six months does not solve the problem. The problem is that if we are to have a presidential system, with all the TV debates and all the power concentrated in Downing Street, we need a constitution designed to elect – and, much more important, to restrain – that president. What we don't want is what we have now – a stream of elected dictators who the vast majority of us don't even get to elect.